Doughnuts are sold in bag and cartons. A bag holds 4 doughnuts and a carton holds 10 doughnuts. Tome buys b bags of doughnuts and c cartons of doughnuts. He buys a total of t doughnuts. Write down the formula for t in terms of b and c

The density function of Y = | X-1 | is given by:

f_Y(y) = {f_X(y + 1), if 0 < y < 1;

        {f_X(1 - y), if 1 < y < 2;

        {0, otherwise.

Continuous distribution is a type of probability distribution that describes the likelihood of a variable taking on any value within a given range, rather than just specific values

If X ~Unif (-1,0), then the density function of Y is given by:

f_Y(y) = {1/2, if 0 < y < 1;

        {1/2, if 1 < y < 2;

        {0, otherwise.

Therefore, Y ~Unif (0,2).

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Answer:

the smallest sample size is 163

Step-by-step explanation:

The computation of the smallest sample size that meets these criteria is shown below:

n = (Z a/2 ×  Standard deviation  ÷ Margin of error ) ^2

Zα/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )

Standard Deviation ( S.D) = 2.6

Margin of error i.e. ME =0.4

n = ( 1.96 × 2.6 ÷ 0.4) ^2

= 163

Hence, the smallest sample size is 163

Answer:

20

Step-by-step explanation:

It is mentioned that Jolyn made $340 in 17 hours last week. In order to evaluate this, you'll have to divide the money earned by the hours worked.

\(\frac{340}{17} =20\)

Therefore, Jolyn makes $20 an hour as 20 x 17 = 340 which is correct,

x⁴ - 8x² + 17 is the function that represents the fog(x).

To find fog(x), we first need to find g(f(x)), which means we need to substitute the expression for f(x) into the expression for g(x):

g(f(x)) = g(x² - 4)

Now, we can substitute the expression for g(x) into the above expression:

g(f(x)) = (x² - 4)² + 1

Expanding the squared term, we get:

g(f(x)) = x⁴ - 8x² + 17

Therefore, fog(x) = g(f(x)) = x⁴ - 8x² + 17.

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Complete question:

f(x) = x² - 4 and g(x)= x^2 + 1  find fog(x).

Answer:

12 units^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

A = 1/2 ( 6 ) * 4

A = 1/2 (24)

    = 12 units^2

The cost price of the shorts is K22.50.

To find the cost price of the shorts, we need to reverse calculate the original price before the markup and taxes were applied.

Let's assume the cost price of the shorts is represented by C.

The markup of 17% is applied to the cost price, which means the selling price (including the markup) is 117% of the cost price.

117% of the cost price C can be calculated as (117/100) * C.

GST (Goods and Services Tax) is also included in the selling price. GST is typically calculated as a percentage of the selling price. In this case, the selling price of the shorts including GST is K29.25.

Since the GST is included in the selling price, we can subtract it from the selling price to obtain the selling price before GST.

Let's assume the GST rate is R% (as a decimal), then the selling price before GST can be calculated as:

Selling price before GST = Selling price - (Selling price × R)

In this case, the selling price before GST is K29.25, and the GST rate is 17% (0.17 as a decimal). Substituting these values into the equation, we have:

K29.25 = Selling price - (Selling price × 0.17)

Simplifying the equation

K29.25 = Selling price × (1 - 0.17)

K29.25 = Selling price × 0.83

Selling price = K29.25 / 0.83

Now we can substitute the selling price in terms of the cost price:

K29.25 / 0.83 = (117/100) × C

Simplifying the equation:

C = (K29.25 / 0.83) × (100/117)

Calculating the cost price C:

C = K22.50

Therefore, the cost price of the shorts is K22.50.

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The length of the park will be 598 meters.

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that two gentlemen are taking their morning walks, beginning from opposite ends of a park. They meet 720 meters away from one of the ends, after which they continue walking. After reaching the end of the park, each turns back. On the way back, they meet at a distance of 400 meters from another end of the park.

The length of the park will be calculated as,

H² = P ² + B²

B² = (720)² - ( 400 )²

B = √ ( 358400 )

B = 598 meters

The length of the park would be 598 meters.

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Answer:

The answer is A.

Step-by-step explanation:

Answer:

y = 14

Step-by-step explanation:

y = k\(\sqrt{x}\)  Solve for k

7 = k\(\sqrt{9}\)

7 = k3  Divide both sides by 3 to solve for k

\(\frac{7}{3}\) = k  

y = kx

y  = \(\sqr\frac{7}{3} }\)\(\sqrt{36}\)

y = \(\frac{7}{3}\)(6)

y = 14

\(\frac{7}{3}\)\((\frac{6}{1})\) is the same thing as \(\frac{7}{1}\)\((\frac{2}{1})\)  I cross canceled the 3 and the 6

\(\frac{14}{1}\) = 14

The regression equation is: y = -0.0068824x + 36.8881

So, the correct option is:

D) None of these.

To compute the regression equation based on the given data, we can use the formulas for slope (b1) and y-intercept (bo):

b1 = (NΣXY - ΣXΣY) / \((N\sum X^2 - (\sum X)^2)\)

bo = (ΣY - b1ΣX) / N

Where:

N = Number of data points (in this case, 11)

ΣX = Sum of all X values (prices)

ΣY = Sum of all Y values (average number of pounds sold per day)

ΣXY = Sum of the product of X and Y values

\(\sum X^2\) = Sum of the squares of X values

Using the provided data:

Ex = 210

Xy = 450

Zcy = 10387

Zz = 7275

Xy = 42471

Let's calculate the required values:

N = 11

ΣX = Ex + Zcy + Zz = 210 + 10387 + 7275 = 17872

ΣY = Xy = 450

ΣXY = Xy = 450

\(\sum X^2 = (Ex)^2 + (Zcy)^2 + (Zz)^2 = (210)^2 + (10387)^2 + (7275)^2 = 239208144\)

Now, substitute these values into the formulas to find b1 and bo:

\(b1 = (11 \times450 - 17872 \times 450) / (11 \times239208144 - (17872)^2)\)

= -14112250 / 2050445128

≈ -0.0068824

bo = (450 - (-0.0068824 \(\times\) 17872)) / 11

= (450 + 122.7790368) / 11

≈ 36.8881

Therefore, the regression equation is:

y = -0.0068824x + 36.8881

So, the correct option is:

D) None of these.

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The complete question may be like:

Over a period of one year, retailer sells widgets at 11 different prices. He Calculates the average number of oiunds sold per day at each different price. From theese data, the following are calculated. Ex = 210, Xy = 450, Zcy = 10387, Zz? 7275 Xy? 42471 Compute the regression equation , SELEC A) y 0.20261x + 0.549951 B) y = 0.549951x + 30.410021 C) y = 0.20261. + 30.410021 D) none of these =b1x + bo.

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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By using normal distribution, we get probability of gains between 0kg to 3kg is 0.2547

What is normal distribution?

A probability distribution known as a "normal distribution" is symmetric about the mean and indicates that data that are close to the mean are more likely to occur than data that are far from the mean.

Given that:

μ= 1.4

σ=4.6

We know the formula of normal distribution is z = (x-μ)/σ

\(P(0 < x < 3)=P(x < 3)-P(x < 0)\)

For \(P(x < 3)\)

\(z=\frac{3-1.4}{4.6} \\z=0.35\)

By using the z-table \(P(x < 3)=0.6368\)

For \(P(x < 0)\)

\(z=\frac{0-1.4}{4.6}\\z=-0.30\)

By using the z-table \(P(x < 0)=0.3821\)

Substituting \(P(x < 3)\) and \(P(x < 0)\) in \(P(0 < x < 3)\)

we get,

\(P(0 < x < 3)=0.6368-0.3821\\P(0 < x < 3)=0.2547\)

Therefore, by using normal distribution, we get probability of gains between 0kg to 3kg is 0.2547

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9514 1404 393

Answer:

  20%

Step-by-step explanation:

The discount was $35 -28 = $7. As a percentage of the original price, that is ...

  $7/$35 × 100% = 20%

Mai's coupon was for a 20% discount.

Answer:

-0.91 = strong, as it is close to -1 and if it's close to -1 that means it is linear.

0.82 = strong. Again, it's approaching 1 and is, therefore, approaching linearity.

-0.49 = moderate

0.26= weak

0.54 = moderate

-0.18 = weak

Step-by-step explanation:

Answer:

5/8 or 0.625 or 62.5%.

Step-by-step explanation:

20/32       Divide top and bottom by 4:-

= 5/8.

Answer:

rose i think ...... . that the answer I think

Answer:

Circle of radius 4

Domain: all reals

Range: r = 4

Symmetric about the y-axis, the x-axis and the origin

Continuous

Bounded

Maximum r-value : 4

No asymptotes

Step-by-step explanation:

right on edge

Answer:

Step-by-step explanation:

Volume = Bh

Turn the shape so the trapezoid is on the bottom/base

h=18   for overall shape

B = area of base, trapezoid

B = 1/2 (b₁ + b₂) h  

b₁ = 11

b₂ = 25

h = 24   for trapezoid

B = 1/2 (11 + 25)(24)

B = 432

V = Bh

V = (432)(18)

V= 7776 in³

Answer: -1536

Step-by-step explanation:

(-2)^6 = 64

(-2)^4 = 16

(-2)^-8 = 1/256

(-2)^6 x (-2)^4 x (-2)^-8 = 4

Your final answer is 4!

Answer: x = 50

Step-by-step explanation:

In the given image, the alternate interior angles are equal. Therefore, 80 + x = 180 - 50 (since straight angles measure 180 degrees). Simplifying this equation, we get 130 + x = 180, which gives us x = 50 degrees. Thus, A||B when x = 50 degrees.

Answer:

The answer is "A" i think not 100% sure

tell me if wrong

To find the other angles in a parallelogram if only one is given then you need to subtract the number with 180 to find the consecutive angles. With the theorem 6-5 opposite angles are congruent, so the opposite side would have the same value.

Answer:

Therefore, you need 2600 pounds of 35% supplement and 1300 - 2600 = -1300 pounds of 10% ration.

Step-by-step explanation:

The unknown variable is x, which is the amount of 35% supplement needed. The other expressions are derived from the given information and the fact that the total amount of solution is 1300 pounds.

The equation from the fourth column is:

0.35x + 0.10(1300 - x) = 0.25(1300)

Solving for x, we get:

x = (0.25(1300) - 0.10(1300)) / (0.35 - 0.10) x = 650 / 0.25 x = 2600

The value of the integral is π(540)^2.

We can change the order of integration as follows:

∫^(∞)(0)∫540∫9y6e−x2+zdxdydz = ∫^(540)(0)∫^∞_0∫^√(9y^6)_(−∞)e−x^2dzdxdy

The limits of z are from −∞ to ∞, but the integrand is an even function of z, so we can simplify the integral by taking the absolute value of the integrand and multiplying it by 2:

∫^(540)(0)∫^∞_0∫^√(9y^6)(−∞)e−x^2dzdxdy = 2∫^(540)_(0)∫^∞_0∫^√(9y^6)_0 e−x^2dzdxdy

We can now evaluate the integral with respect to z:

2∫^(540)_(0)∫^∞_0[√π/2 - √π/2erf(−√x^2+z)/2]|^√(9y^6)_0 dxdy

where erf is the error function.

Substituting the limits of integration and simplifying, we get:

2∫^(540)_(0)∫^∞_0[√π/2 - √π/2erf(−3y^3/√2x)/2]dxdy

Next, we can evaluate the integral with respect to x:

2∫^(540)_(0)[√π/2(x - √2/3y^3erf(−3y^3/√2x))]|^∞_0 dy

Since the limits of integration with respect to x are from 0 to ∞, the first term in the square brackets evaluates to ∞, and the second term evaluates to √π/2. Therefore, the integral reduces to:

2∫^(540)_(0)√π/2 dy = π(540)^2

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5 "Always." Consecutive angles of a rectangle are always congruent.

6 "Never." A parallelogram is not always a square.

7 "Sometimes." In a rhombus, the diagonals are always perpendicular bisectors of each other, but they are not always congruent.

8 "Always." A rectangle has congruent sides, but not necessarily all four sides.

9 Given: ABCD is a parallelogram

To prove: AABC = ACDA

Proof:

AB || DC (definition of parallelogram)

AD || BC (definition of parallelogram)

∠ABC = ∠CDA (alternate interior angles)

AC = AC (reflexive property)

∠BCA = ∠DAC (alternate interior angles)

Therefore, AABC = ACDA (ASA congruence theorem)

10 Given: TRAP is an isosceles trapezoid

To prove: AAPR ARTA

TR = AP (definition of isosceles trapezoid)

∠APT = ∠ATR (alternate interior angles)

∠PAR = ∠RTA (alternate interior angles)

∠PAR = ∠APT (angles at a point)

Therefore, AAPR ARTA (AA congruence theorem)

Consecutive angles of a rectangle are always congruent. This is a property of rectangles that is true for every rectangle.

A square is a specific type of parallelogram that has all four sides congruent and all four angles right angles.

A rectangle has two pairs of opposite sides that are congruent, but the adjacent sides may have different lengths. This is a defining characteristic of rectangles, and it is always true for every rectangle.

The ASA congruence theorem states that two triangles are congruent if two angles and the included side of one triangle are congruent to the two angles and the included side of the other triangle. In this case, ∠ABC and ∠CDA are congruent by (3), AC is congruent by (4), and ∠BCA and ∠DAC are congruent by (5). Therefore, AABC = ACDA by the ASA congruence theorem.

The AA congruence theorem states that two triangles are congruent if two angles of one triangle are congruent to two angles of the other triangle, and the side between those angles is congruent in both triangles

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Answer:

\(E(Y) = 750\)

Step-by-step explanation:

Given

Sample Size = 2500

Percentage = 30%

Required

Calculate Mean of Y

Mean or Expected Value is calculated as thus;

\(E(Y) = np\)

Where E(Y) represents the mean

n represents the sample size (or population)

p represents the success probability

\(n = 2500 ; p = 30%\)%

\(p = \frac{30}{100} = 0.3\)

So,

\(E(Y) = 2500 * 0.3\)

\(E(Y) = 750\)

Hence, the mean value of Y is 750

Using the concept of whole numbers, it is found that there are 42 whole numbers that are greater than 21 to the power of 2 and less than 22 to the power of 2.

A whole number is a countable number, that is, 1, 2, 3, 4, ....

In this problem, the numbers are:

21^2 = 441.

22^2 = 484.

The amount of numbers between them, excluding them, is given by:

484 - 441 - 1 = 42

There are 42 whole numbers that are greater than 21 to the power of 2 and less than 22 to the power of 2.

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The total measurements of the roof in square feet as required to be determined in the task content is; 2649 ft².

It follows from the task content that the total area of the roof as given in the task content is to be determined.

On this note, the area of the roof is the total area of the 71ft by 39 ft rectangle minus the area of the shaded region with dimensions 15 ft by 8 ft.

Therefore;

Area = (71 × 39) - (15 × 8)

= 2649 ft².

Ultimately, the total area measure of the roof in square feet is; 2649 square feet.

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